We consider the sinusoid regression experiment [1]}, a multi-task representation learning problem where each task \(\mathcal {T}_i\)  is a regression problem \(y = t_i(x) = a_i \sin (x - \phi _i)\) . We uniformly sample the amplitude \(a_i \in [0.1, 5]\) , frequency and phase \(\phi _i \in [0, \pi ]\)  for each task. We use \(n=3\)  training tasks and 3 testing tasks, with 2 "easy tasks" \((a_i \in [0.1, 1.05])\)  and one "hard tasks" \((a_i \in [4.95, 5])\)  for each set. We use easy and hard tasks following the setup in [2]}. During training, for each task \(i\) , the learner is given samples \((x, y)\) , \(x \in [-5, 5]\) . The goal is to learn a function approximating \(t_i\)  as best as possible in the mean squared error sense.
